Electron density

In chemistry electron density is the measure of the probability of an electron being present at a specific location. According to quantum mechanics, due to the uncertainty principle on an atomic scale the exact location of an electron cannot be predicted, only the probability of its being at a given position; therefore electrons in atoms and molecules act as if they are 'smeared out' in space. For one-electron systems, the electron density at any point is proportional to the square magnitude of the wavefunction. In molecules, regions of large electron density are usually found around the atom, and its bonds. In de-localized or conjugated systems, such as phenol, benzene and compounds such as hemoglobin and chlorophyll, the electron density is significant in an entire region, i.e., in benzene they are found above and below the planar ring. This is sometimes shown diagrammatically as a series of alternating single and double bonds. In the case of phenol and benzene, a circle inside a hexagon shows the delocalized nature of the compound. This is shown below: In compounds with multiple ring systems which are interconnected, this is no longer accurate, so alternating single and double bonds are used. In compounds such as chlorophyll and phenol, some diagrams show a dotted or dashed line to represent the delocalization of areas where the electron density is higher next to the single bonds. Conjugated systems can sometimes represent regions where electromagnetic radiation is absorbed at different wavelengths resulting in compounds appearing coloured. In polymers, these areas are known as chromophores. In quantum chemical calculations, the electron density, ρ(r), is a function of the coordinates r, defined so ρ(r)dr is the number of electrons in a small volume dr. For closed-shell molecules, ρ ( r ) {displaystyle ho (mathbf {r} )} can be written in terms of a sum of products of basis functions, φ: where P is the density matrix. Electron densities are often rendered in terms of an isosurface (an isodensity surface) with the size and shape of the surface determined by the value of the density chosen, or in terms of a percentage of total electrons enclosed. Molecular modeling software often provides graphical images of electron density. For example, in aniline (see image at right). Graphical models, including electron density are a commonly employed tool in chemistry education. Note in the left-most image of aniline, high electron densities are associated with the carbons and nitrogen, but the hydrogens with only one proton in their nuclei, are not visible. This is the reason that X-ray diffraction has a difficult time locating hydrogen positions. Most molecular modeling software packages allow the user to choose a value for the electron density, often called the isovalue. Some software also allows for specification of the electron density in terms of percentage of total electrons enclosed. Depending on the isovalue (typical units are electrons per cubic bohr), or the percentage of total electrons enclosed, the electron density surface can be used to locate atoms, emphasize electron densities associated with chemical bonds , or to indicate overall molecular size and shape. Graphically, the electron density surface also serves as a canvas upon which other electronic properties can be displayed. The electrostatic potential map (the property of electrostatic potential mapped upon the electron density) provides an indicator for charge distribution in a molecule. The local ionization potential map (the property of local ionization potential mapped upon the electron density) provides an indicator of electrophilicity. And the LUMO map (lowest unoccupied molecular orbital mapped upon the electron density) can provide an indicatory for nucleophilicity.